Geodesic
Boundary properties of arbitrary functions
Izvestiya. Mathematics , Tome 1 (1967) no. 1, pp. 1-12

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We study the dependence between various sets of limiting boundary values of an arbitrary function $f$ of $z$. In particular we show that the Plesner theorem on angular boundary values of analytic functions generalizes in a natural way to arbitrary functions. 
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     author = {E. P. Dolzhenko},
     title = {Boundary properties of arbitrary functions},
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E. P. Dolzhenko. Boundary properties of arbitrary functions. Izvestiya. Mathematics , Tome 1 (1967) no. 1, pp. 1-12. http://geodesic.mathdoc.fr/item/IM2_1967_1_1_a0/